In the US?<p>This has to vary per country. Here in the UK I think usually you set up a standing order, that is an automatic scheduled bank transfer for a set amount every month. You can do that online and these days the transfer is instant, and it does not require any third party services or fees.
I had this at an apartment once. They were a large enough company that they did this and it was great. Now I have to mail a check to my current one. It's a shame, but probably is related to scale.
I assume that you can for some landlords. I might be in the minority, but I can track and pay my mortgage online; I don't see why it's impossible for rent payments.